The answer to your immediate issue is that you need to use double quotes instead of single quotes if you want a variable value to interpolate into a string. Your line should therefore read $table_hash{"$n,0"} = $m;. See Quote and Quote like Operators in perlop.

You are using compound keys to emulate a multidimensional array in your code, which is very Perl 4. With the addition of array references (a couple decades ago), I would do this with something like:

#!usr/bin/perl
use strict;
use warnings;
use Data::Dumper;

my @table = (
    ['X', 'Y', 'Z'],
);

print Dumper \@table;

my $m=0;
foreach my $n (0..3) {
    $table[$n][0] = $m++;
};

print Dumper \@table;
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See perlreftut.